We study the online graph exploration problem proposed by Kalyanasundaram and Pruhs (1994) and prove a constant competitive ratio on minor-free graphs. This result encompasses and significantly extends the graph classes that were previously known to admit a constant competitive ratio. The main ingredient of our proof is that we find a connection between the performance of the particular exploration algorithm Blocking and the existence of light spanners. Conversely, we exploit this connection to construct light spanners of bounded genus graphs. In particular, we achieve a lightness that improves on the best known upper bound for genus g>0 and recovers the known tight bound for the planar case (g=0).

翻译：我们研究Kalyanasundaram和Pruhs（1994）提出的在线图探索问题，并证明了在无小结构图中存在常数竞争比。这一结果涵盖并显著扩展了先前已知具有常数竞争比的图类。证明的主要要素在于，我们发现了特定探索算法Blocking的性能与轻量spanner存在性之间的关联。反之，我们利用这一关联构造了有界亏格图的轻量spanner。特别地，我们实现的轻量性改进了已知的亏格g>0情况的上界，并恢复了平面情况（g=0）的已知紧界。